CSCE 590E Spring 2007

1. CSCE 590E Spring 2007 Animation and AI By Jijun Tang

2. Announcements • April 16th/18th: demos • Show progress/difficulties/change of plans • USC Times will have reporters in the class • High school outreach • Anyone can contact their high school admin to arrange direct talks to students • Of course, in SC only

3. Homework • P 655 questions 1 and 2 • 5 points total • Due April 16th

4. What is animation? • Animation is from the latin “anima” or soul • To give motion • Means to give life Anything you can do in your game to give it more “life” through motion (or lack of motion).

5. Different types of animation • Particle effects • Procedural / Physics • “Hard” object animation (door, robot) • “Soft” object animation (tree swaying in the wind, flag flapping the wind) • Character animation

6. Skeletal Hierarchy • The Skeleton is a tree of bones • Often flattened to an array in practice • Top bone in tree is the “root bone” • May have multiple trees, so multiple roots • Each bone has a transform • Stored relative to its parent’s transform • Transforms are animated over time • Tree structure is often called a “rig”

7. Example

8. The Transform • “Transform” is the term for combined: • Translation • Rotation • Scale • Shear • Can be represented as 4x3 or 4x4 matrix • But usually store as components • Non-identity scale and shear are rare • Optimize code for common trans+rot case

9. Examples

10. Three rotations about three axes Intuitive meaning of values Euler Angles

11. Problems • Euler Angles Are Evil • No standard choice or order of axes • Singularity “poles” with infinite number of representations • Interpolation of two rotations is hard • Slow to turn into matrices • Use matrix rotation

12. Rotation Matrix

13. Quaternions on Rotation • Represents a rotation around an axis • Four values <x,y,z,w> • <x,y,z> is axis vector times sin(angle/2) • w is cos(angle/2) • No singularities • But has dual coverage: Q same rotation as –Q • This is useful in some cases! • Interpolation is fast

14. Quaternion to Matrix • To convert a quaternion to a rotation matrix:

15. Matrix to Quaternion • Matrix to quaternion is doable • It involves a few ‘if’ statements, a square root, three divisions, and some other stuff • Search online if interested

16. Pose

17. Storage – The Problem • 4x3 matrices, 60 per second is huge • 200 bone character = 0.5Mb/sec • Consoles have around 32-64Mb (Xbox and PS3 have larger, but still limited) • Animation system gets maybe 25% • PC has more memory • But also higher quality requirements

18. Keyframes • Motion is usually smooth • Only store every nth frame • Store only “key frames” • Linearly interpolate between keyframes • Inbetweening or “tweening” • Different anims require different rates • Sleeping = low, running = high • Choose rate carefully

19. Linear Interpolation

20. Higher-Order Interpolation • Tweening uses linear interpolation • Natural motions are not very linear • Need lots of segments to approximate well • So lots of keyframes • Use a smooth curve to approximate • Fewer segments for good approximation • Fewer control points • Bézier curve is very simple curve

21. Bézier Curves (2D & 3D) • Bézier curves can be thought of as a higher order extension of linear interpolation p1 p1 p2 p3 p1 p0 p0 p0 p2

22. Non-Uniform Curves • Each segment stores a start time as well • Time + control value(s) = “knot” • Segments can be different durations • Knots can be placed only where needed • Allows perfect discontinuities • Fewer knots in smooth parts of animation • Add knots to guarantee curve values • Transition points between animations • “Golden poses”

23. Playing Animations • “Global time” is game-time • Animation is stored in “local time” • Animation starts at local time zero • Speed is the ratio between the two • Make sure animation system can change speed without changing current local time • Usually stored in seconds • Or can be in “frames” - 12, 24, 30, 60 per second

24. Scrubbing • Sample an animation at any local time • Important ability for games • Footstep planting • Motion prediction • AI action planning • Starting a synchronized animation • Walk to run transitions at any time • Avoid delta-compression storage methods • Very hard to scrub or play at variable speed

25. Animation Blending • The animation blending system allows a model to play more than one animation sequence at a time, while seamlessly blending the sequences • Used to create sophisticated, life-like behavior • Walking and smiling • Running and shooting

26. Blending Animations • The Lerp • Quaternion Blending Methods • Multi-way Blending • Bone Masks • The Masked Lerp • Hierarchical Blending

27. Motion Extraction • Moving the Game Instance • Linear Motion Extraction • Composite Motion Extraction • Variable Delta Extraction • The Synthetic Root Bone • Animation Without Rendering

28. Moving the Game Instance • Game instance is where the game thinks the object (character) is • Usually just • pos, orientation and bounding box • Used for everything except rendering • Collision detection • Movement • It’s what the game is! • Must move according to animations

29. Linear Motion Extraction • Find position on last frame of animation • Subtract position on first frame of animation • Divide by duration • Subtract this motion from animation frames • During animation playback, add this delta velocity to instance position • Animation is preserved and instance moves • Do same for orientation

30. Problems • Only approximates straight-line motion • Position in middle of animation is wrong • Midpoint of a jump is still on the ground! • What if animation is interrupted? • Instance will be in the wrong place • Incorrect collision detection • Purpose of a jump is to jump over things!

31. Composite Motion Extraction • Approximates motion with circular arc • Pre-processing algorithm finds: • Axis of rotation (vector) • Speed of rotation (radians/sec) • Linear speed along arc (metres/sec) • Speed along axis of rotation (metres/sec) • e.g. walking up a spiral staircase

32. Benefits and Problems • Very cheap to evaluate • Low storage costs • Approximates a lot of motions well • Still too simple for some motions • Mantling ledges • Complex acrobatics • Bouncing

33. Variable Delta Extraction • Uses root bone motion directly • Sample root bone motion each frame • Find delta from last frame • Apply to instance pos+orn • Root bone is ignored when rendering • Instance pos+orn is the root bone

34. Benefits • Requires sampling the root bone • More expensive than CME • Can be significant with large worlds • Use only if necessary, otherwise use CME • Complete control over instance motion • Uses existing animation code and data • No “extraction” needed

35. The Synthetic Root Bone • All three methods use the root bone • But what is the root bone? • Where the character “thinks” they are • Defined by animators and coders • Does not match any physical bone • Can be animated completely independently • Therefore, “synthetic root bone” or SRB

36. The Synthetic Root Bone (2) • Acts as point of reference • SRB is kept fixed between animations • During transitions • While blending • Often at centre-of-mass at ground level • Called the “ground shadow” • But tricky when jumping or climbing – no ground! • Or at pelvis level • Does not rotate during walking, unlike real pelvis • Or anywhere else that is convenient

37. Animation Without Rendering • Not all objects in the world are visible • But all must move according to anims • Make sure motion extraction and replay is independent of rendering • Must run on all objects at all times • Needs to be cheap! • Use LME & CME when possible • VDA when needed for complex animations

38. Mesh Deformation • Find Bones in World Space • Find Delta from Rest Pose • Deform Vertex Positions • Deform Vertex Normals

39. Find Bones in World Space • Animation generates a “local pose” • Hierarchy of bones • Each relative to immediate parent • Start at root • Transform each bone by parent bone’s world-space transform • Descend tree recursively • Now all bones have transforms in world space • “World pose”

40. Example

41. Find Delta from Rest Pose • Mesh is created in a pose • Often the “da Vinci man” pose for humans • Called the “rest pose” • Must un-transform by that pose first • Then transform by new pose • Multiply new pose transforms by inverse of rest pose transforms • Inverse of rest pose calculated at mesh load time • Gives “delta” transform for each bone

42. Deform Vertex Positions • Each vertex has several bones affect it (the number is generally set to <=4). • Vertices each have n bones • n is usually 4 • 4 bone indices • 4 bone weights 0-1 • Weights must sum to 1 • Deformation usually performed on GPU • Delta transforms fed to GPU • Usually stored in “constant” space

43. Deform Vertex Positions (2) vec3 FinalPosition = {0,0,0}; for ( i = 0; i < 4; i++ ) { int BoneIndex = Vertex.Index[i]; float BoneWeight = Vertex.Weight[i]; FinalPosition += BoneWeight * Vertex.Position * PoseDelta[BoneIndex]); }

44. Deform Vertex Normals • Normals are important for shading and are done similarly to positions • When transformed, normals must be transformed by the inverse transpose of the transform matrix • Translations are ignored • For pure rotations, inverse(A)=transpose(A) • So inverse(transpose(A)) = A • For scale or shear, they are different • Normals can use fewer bones per vertex • Just one or two is common

45. Inverse Kinematics • FK & IK • Single Bone IK • Multi-Bone IK • Cyclic Coordinate Descent • Two-Bone IK • IK by Interpolation

46. FK & IK • Most animation is “forward kinematics” • Motion moves down skeletal hierarchy • But there are feedback mechanisms • Eyes track a fixed object while body moves • Foot stays still on ground while walking • Hand picks up cup from table • This is “inverse kinematics” • Motion moves back up skeletal hierarchy

47. Example of Forward Kinematics • http://www.cs.nyu.edu/~lyl209/hw4/doll/

48. Example of Inverse Kinematics

49. Single Bone IK • Orient a bone in given direction • Eyeballs • Cameras • Find desired aim vector • Find current aim vector • Find rotation from one to the other • Cross-product gives axis • Dot-product gives angle • Transform object by that rotation

50. Multi-Bone IK • One bone must get to a target position • Bone is called the “end effector” • Can move some or all of its parents • May be told which it should move first • Move elbow before moving shoulders • May be given joint constraints • Cannot bend elbow backwards